240 NOTES. 



We have, from (1), 



dT dT 



uE+ ... +A+ ... = -7- tt + ... + -=- +..., 

 du dp r 



= 2T ........ . ........................ (2), 



since T is a homogeneous quadratic function. Performing the arbitrary 

 variation 8 on both sides of (2) we find 



and thence, making use of (1), 



, s 



-j- 016 + ... + -7- d + .... 



aw c^p r 



Since the variations $u, Sp, &c. are here independent, we have 



,_dT dT 



*~du&amp;gt; ~&amp;gt; X ~~d I j ~ t 



the formulae to be proved. 



